I understand that the most relevant comparator of the impact of Covid-19 is the excess death rates against a 5 year average, which takes out any differences in methods of recording a Covid death of the type you describe.
The ONS has recently published an analysis of the all-cause mortality across European countries which includes breakdown for the different parts of the UK. Table 4 shows the percentage increase between England and Wales which is significant and help understanding of the relative success in managing the virus across the UK.
https://www.ons.gov.uk/peoplepopulat...uarytojune2020